1. Field of the Invention
The present invention relates to an image forming optical system such as a microscope, a camera, and an endoscope, a focusing optical system such as an optical pickup and a semiconductor exposing apparatus, and a guided-wave optical system such as an optical integrated circuit, and an optical fiber.
2. Description of the Related Art
In recent years, a resolution power of an image detecting apparatus in which an image pickup optical system such as a microscope, a camera, and an endoscope is used has been improved. Particularly, in a field of microscopes and optical recording, an almost no aberration optical system has been realized, and a resolution power as an image pickup optical system has been constrained mainly by a diffraction limit of a visible light.
On the other hand, as it has been disclosed in the Non-Patent Literature ‘Physical Review Letters’, Volume 85, Page 3966 (2000), by J. B. Pendry, an optical material in which a refractive index takes a negative value (hereinafter, called appropriately as a ‘negative refraction material’) has been realized. It has been proposed that when the negative refraction material is used, it is possible to form an image having an ultra high resolution beyond the diffraction limit (hereinafter, called appropriately as ‘perfect imaging’).
As it has been disclosed in Non-Patent Literature ‘Physical Review Letters’, Volume 85, Page 3966 (2000), by J. B. Pendry, even in a case other than a case in which the refractive index takes a negative value, when a real part of a permittivity or a permeability is a negative value, for electromagnetic waves of a specific polarization state, a negative refraction phenomenon is observed.
Moreover, as it has been disclosed in Non-Patent Literature ‘Physical Review B’, Volume 62, Page 10696 (2000), by M. Notomi, in a periodic structure such as a photonic crystal, as a result of a photonic band being folded in a reciprocal lattice space, irrespective of being a material having each of the refractive index, the permittivity, and the permeability a positive value, the negative refraction phenomenon has been observed for electromagnetic waves of a specific wavelength and a specific polarization state.
In view of the abovementioned circumstances, in this patent specification, a material which exhibits a negative refraction response for specific electromagnetic waves is called as a ‘material exhibiting negative refraction’. It is needless to mention that a term ‘material exhibiting negative refraction’ is a concept having a wider sense than the negative refraction material.
Apart from the photonic crystals mentioned above, materials such as a metallic thin film, a chiral substance, photonic crystals, a metamaterial, a left-handed material, backward wave material, and a negative phase velocity medium have been known as the materials exhibiting negative refraction.
For a material having a negative value for both the permittivity and the permeability, the refractive index is also a negative value. Furthermore, such materials satisfy Snell's law, when an angle of refraction is extended up to a negative value.
In an image formation (focusing) by a normal lens, a refractive index of a lens has to differ from a refractive index of an outside of the lens, and a lens surface has to be curved, are two requirements.
Whereas, a flat plate which is made of a material exhibiting negative refraction (hereinafter, called appropriately as a “negative refraction lens”) can focus the light irrespective of a radius of curvature of the surface being infinite, in other words, in spite of being a flat surface. FIG. 32 shows an image formation relationship by a negative refraction lens 31. Light from an object point 33 on an object plane 32 is focused at an image point 35 on an image plane 34, by the negative refraction lens 31.
In an image forming optical system such as a microscope, an upper-limit value of a theoretical resolution is determined by a diffraction limit. As it has been described in a textbook of optics such as Non-Patent Literature ‘Optics’, 4th edition (Addison-Wesley, Reading, Mass., 2002) by E. Hecht, according to a Rayleigh criterion, a minimum distance between two resolvable points is λ/NA. Here, λ is a usable wavelength, and NA is a numerical aperture. Moreover, for a structure smaller than the diffraction limit, it can not be resolved by an optical system.
Moreover, a microscope and an optical pickup which improve the resolution by using an objective lens of a liquid immersion, an oil immersion, or a solid immersion (by using an objective lens such as a liquid-immersion objective lens, an oil-immersion objective lens, and a solid-immersion objective lens), has been proposed. An effective NA is increased in these lenses. Accordingly, a value of λ/NA equivalent to the diffraction limit is made small. Here, the numerical aperture NA cannot be increased more than a refractive index of a medium on which the object plane is disposed. Therefore, an upper limit for the numerical aperture is about 1.5 to 2.0.
In this patent specification, when an electromagnetic wave including the light is expressed in an amplitude and phase as a wave, light for which all components of a wave-number vector included in a phase are real numbers is to be called as propagating light, and light for which at least one component is not a real number is to be called as an evanescent wave. Light which has emitted from one point in space includes two light waves namely propagating light which reaches up to a far distance, and evanescent waves which are attenuated at a distance of about a wavelength.
In Non-Patent Literature ‘Physical Review Letters’, Volume 85, Page 3966 (2000), by J. B. Pendry, which was disclosed in recent years, a negative materials performs a reverse amplification of the evanescent waves which are supposed to be attenuated in a direction in which a component of the wave-number vector is not originally a real number, is disclosed. Therefore, in the image formation by the negative refraction lens 31 shown in FIG. 32, the amplitude of the evanescent waves on the image plane 34 is shown to be restored to the same quantity as on the object plane 32.
In other words, in an optical system shown in FIG. 32, both the propagating light and the evanescent waves are transferred from the object plane 32 to the image plane 34. Therefore, information of the object point 33 is reproduced perfectly at the image point 35. This means that when an image forming optical system in which the negative refraction lens 31 is used, is used, the perfect imaging in which the diffraction limit is not restricted, is possible.
The perfect imaging mentioned above is not true only in theoretical terms. The negative refraction lens was made, and results of experiments have been reported. For example, in Non-Patent Literature ‘Physical Review Letters’, Volume 84, Page 4184 (2000), by D. R. Smith et al., a metamaterial in which, a rod and a coil made of a metal, smaller than the wavelength are arranged periodically, has been made. Functioning of such metamaterial as a negative refraction lens in a microwave region has been reported.
Moreover, in Non-Patent Literature ‘Physical Review B’, Volume 62, Page 10696 (2000), by M. Notomi, a method of making a negative refraction material by using a photonic crystal has been disclosed. For example, in a photonic crystal in which, air rods are arranged in a hexagonal lattice form in a dielectric substance, an effective refractive index in a photonic band becomes isotropic and negative. With respect to a frequency band which is suitable for such photonic band, the photonic crystal can be considered as a negative refraction material.
Moreover, it has been known that for many metals, a real part of the permittivity for visible light becomes positive. For example, according Non-Patent Literature ‘Handbook of Advanced Optical Technology’ by J. Tsujiuchi et al., (published by Asakura Shoten, Japan 2000), silver exhibits a negative permittivity for light of a wavelength in a range of 330 nm to 900 nm. Furthermore, it has been known that a gyrotropic material or a chiral substance having a spiral (helical) structure, exhibits negative refraction under predetermined conditions. In this manner, when a negative refraction lens formed by a negative refraction material is used, it is possible to realize an image forming optical system of ultra high resolution (perfect imaging) which is not constrained by the diffraction limit.
An image formation by a normal lens is shown in FIG. 30. Even when it is a lens of no matter how large the aperture is, it is not possible to make the numerical aperture NA to be greater (higher) than a refractive index of a medium which fill a space on an object side or an image side. In FIG. 30, a lens is kept in air of a refractive index nA, and by using an angle θ1 between a light ray which passes through an edge portion of the aperture and an optical axis of the lens, the numerical aperture expressed by NA=nA sin θ1 can never go beyond nA (almost same as 1).
FIG. 31 is a diagram in which an image formation performance by the lens in FIG. 30 is expressed in terms of a modulation transfer function (MTF). A wave-number vector of a light wave bearing a transfer of an image is let to be k, and a component kv perpendicular to that optical axis is taken on a horizontal axis. Since alight wave component is greater than a wave number expressed by k0=2π/λ(λ is a wavelength of the light wave) becomes an evanescent wave, kv doesn't reach the image plane.
Since a light wave component in which kv is smaller than k0 but greater than k0 sin θ1 is vignetted by a pupil (aperture stop) of the lens, can not reach the image plane, as expected. Eventually, since only a light wave component which satisfies a relationship kv≦k0 sin θ1 can contribute to the image formation, a point image is spread to about wavelength. Moreover, in an actual lens, greater the kv, the MTF is declined due to reflection and scattering at a lens surface.
FIG. 32 is a diagram for describing the image formation by the negative refraction lens 31. As it is shown by dotted lines in the diagram, light emitted from the object point 33 on the object plane 32 forms an image on the image point 35 on the image plane 34, after being refracted at two surfaces of the negative refraction lens 31.
As it has been disclosed in Non-Patent Document ‘Physical Review Letters’, Volume 85, Page 3966 (2000) by J. B. Pendry, the negative refraction lens 31 can form an image by since not only the propagating light but also the evanescent light , MTF becomes 1 for all the values of kv as shown in FIG. 33. This means that the point image becomes a point. Such a lens is called as a perfect lens, and a phenomenon is called as a perfect imaging.
Even when it is a perfect imaging which is imperfect due to various restrictions (such as a shape error, a refractive index error, and an absorption) in making practically of the negative refraction lens, when it shows superior image forming performance than a conventional lens restricted by the diffraction limit, it is called as a perfect imaging effect.
However, in a case of making the negative refraction lens in reality, a size of the lens in a direction perpendicular to the optical axis has to be finite. Therefore, propagating light which is vignetted by a pupil of the negative refraction lens such as a light ray 36 and a light ray 37 in FIG. 32, is lost from the optical system without contributing to the image formation. When a minimum angle of emergence of a light ray vignetted by a pupil on an object side surface and an image side surface of the negative refraction lens is let to be θ2 and θ3 respectively, then θ2>θ3 in a situation in FIG. 32.
In other words, when an angle of emergence θ of a light ray from the object point increases gradually and exceeds θ3, the light ray is incident on the negative refraction lens, but either exits from a lens side surface as the light ray 37, or is absorbed. When the angle of emergence θ increases gradually and exceeds θ2, the light ray is not incident on the negative refraction lens, as the light ray 36.
A diagram in which the image formation performance is expressed in terms of the MTF upon taking into consideration the vignetting by the pupil of the negative refraction lens 31 in such manner is FIG. 34. Information of a frequency side higher than k0 is transferred by the imaging effect of the evanescent wave, but a component of the propagating light from a lower value out of k0 sin θ2 and k0 sin θ3, up to k0 is lost.
The negative refraction lens has a rare capability of amplifying the evanescent wave, which is impossible in any conventional technology. However, even when it is possible to form an image of an evanescent wave bearing fine information, taking into consideration a restriction in reality that the size of the lens is finite, the perfect imaging effect is lost due to the vignetting by the pupil.